On the higher order mixed structure functions in laboratory shear flow

Abstract

Structure functions to order 8 are determined from the longitudinal and transverse velocity fluctuations measured at a single point in high Reynolds number laboratory shear flow. We examine the relationship between mixed structure functions (which are explicitly zero in isotropic flow), and those of the longitudinal and transverse structure functions. Our results confirm recent findings using SO(3) symmetry decomposition [S. Kurien and K. R. Sreenivasan, Phys. Rev. E 62, 2206 (2000)] that show that the mixed structure functions have larger scaling exponents than those of the single component structure functions, i.e., the j=2 anisotropic sector structure function scaling exponent is greater than that of the j=0 isotropic sector. However, we also show that the ratio of the j=2 to j=0 sector scaling exponents systematically decreases with increasing order, suggesting that at higher orders there is persistence of anisotropy at the smallest scales. Difficulties in the analysis due to the difference in scaling exponents of the transverse and longitudinal structure functions are addressed.